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Suppose that an inverse limit of finite flat morphisms $X_k\to S$ of qcqs schemes, with affine transition maps, is $X\to S$, such that a closed fiber of $X\to S$ is finite.
Is $X\to S$ finite?
If true, flatness should be the whole point.
Suppose that an inverse limit of finite flat morphisms $X_k\to S$ of qcqs schemes, with affine transition maps, is $X\to S$, such that a closed fiber of $X\to S$ is finite. Is $X\to S$ finite?
If true, flatness should be the whole point.
Suppose that an inverse limit of finite flat morphisms $X_k\to S$ of qcqs schemes, with affine transition maps, is $X\to S$, such that a closed fiber of $X\to S$ is finite.
Suppose that an inverse limit of finite flat morphisms $X_k\to S$ of qcqs schemes, with affine transition maps, is $X\to S$, such that a closed fiber of $X\to S$ is finite. Is $X\to S$ finite?
